[HN Gopher] A guide for people who want to self-study the basics...
___________________________________________________________________
A guide for people who want to self-study the basics of computer
science
Author : tsingy
Score : 217 points
Date : 2023-06-18 13:43 UTC (9 hours ago)
(HTM) web link (github.com)
(TXT) w3m dump (github.com)
| ggr2342 wrote:
| For understanding higher math I have found this primer course
| extremely useful:
|
| Introduction to Mathematical Thinking by Keith Devlin (Stanford)
| https://www.coursera.org/learn/mathematical-thinking
| Zolomon wrote:
| I read this book which helped me understand what it finally
| meant to think mathematically. Highly recommended, Keith is a
| fantastic lecturer.
| totierne2 wrote:
| I am looking for a bottle of computer science motivation for my
| 16 year old. I do an hour a week coding with him. It is not
| enough, he does no coding in between times. There are other
| things he prioritises ahead of coding. (School, music, YouTube
| videos, and chess.)
| qup wrote:
| Chess-related chatbot? Something his friends/chat room/twitch
| can interact with, that has some kind of chess functionality.
|
| Look up "aol chat coms" for inspiration from the 90s.
|
| There used to be bots that played a scrambler game in AOL chat,
| you could make a chess-related one.
| Swizec wrote:
| Maybe your son is not into coding and that's okay. This is not
| a great profession to be in if you don't enjoy it.
| gigatexal wrote:
| Let him find his passion. Don't force him into programming.
| There's plenty in the tech space that needs doing. And there's
| even more in life that he can do to earn a living that's not
| tech related.
| hooverd wrote:
| Imagine doing science, engineering, or mathematics. Might as
| well be getting an English degree.
| mywacaday wrote:
| Pushing him to do something weekly that he doesn't sound
| interested in at the moment will only push him away from it in
| the longer term. Maybe try programming something that overlaps
| with his other interests that deepens his understanding of both
| subjects.
| [deleted]
| tsingy wrote:
| Try finding something that he likes, that could be enhanced
| with programming to start with. Mine was fantasy basketball,
| doing it with the help of computers is so much better than by
| hand.
| Cerium wrote:
| And keep it approachable! There is nothing wrong with writing
| that fantasy basketball calculator as a spreadsheet.
|
| Spreadsheets have many advantages that get overlooked by
| pushing for a "real language" while jump into a programming
| language involves learning a lot of new concepts at once.
|
| For example, spreadsheets make all the memory visible at
| once. It makes sense like a piece of paper. You also have
| intuitive understanding of your algorithms memory
| consumption. Computing something for N by N obviously uses
| N^2 cells. Many problems will be solved in 2^n which will
| mean dragging down that cell for a short while at low values
| and suddenly a very long while.
| gareve wrote:
| create a music or YouTube bot together
| LocalH wrote:
| Then stop focusing on trying to get him to code, and focus on
| his music, his chess, his YouTube videos ( _especially_ if he
| has aspiration to be a content creator rather than a passive
| consumer), and his academics. Maybe related to one of those
| things, you could gently try to build a bridge between them and
| coding. However, _don 't force it_. If you force it, you're
| essentially going to be raising someone who _hates_ programming
| because "it's that shit my mom/dad forced me to do when I had
| no interest in doing it, I really wanted to be developing my
| chess game instead".
| voz_ wrote:
| This is good advice if you live in a Hollywood movie fantasy,
| or are insanely rich. Otherwise this is bad advice.
|
| A parents job is to steer their kids not into superficial
| happiness found through whatever interested them at 16, but
| to actual long term happiness achieved through fulfillment,
| accomplishment, stability, and belonging.
|
| If I ignored CS pushed by my father to focus on whatever
| interested me at 16 (pot, girls, metal music, wow), I'm not
| sure where id be, but I imagine it would be worse off.
| cinntaile wrote:
| It's neither good nor bad advice. It will depend on the
| kid. Some will respond like you, while some will respond
| like the commenter above you explains.
| waboremo wrote:
| I believe you interpreted their comment as a sort of let
| them drown in hedonism moment, but from what I'm getting
| it's really just encouraging giving your kid space to find
| the joy themselves. You can encourage new forms or methods
| to see if it'll stick but you still have to let them be
| their own person. Forcing anything will just make your kid
| resent that entirely, and for a lot of parents they don't
| even realize this resentment of [subject/task/etc] also
| turned into a resentment of the parent.
|
| Also I think you're too pessimistic about your past
| potential. You could have made a great musician, esports
| pro, hell there are even some successful marijuana
| companies now! I don't say this to stoke the flames of what
| ifs, but instead to highlight that it wasn't exactly your
| father's push for CS that is the only reason for your
| success. You should absolutely take some responsibility for
| committing and be proud of that, of course you can
| definitely attribute your understanding of why commitment
| is important to your father if that holds true!
|
| Now that's good advice, teach your kids the importance of
| integral foundations like commitment, don't obsess over
| which specific field it is.
| dkjaudyeqooe wrote:
| Appeal to his music interests. This book looks pretty good and
| uses free tools:
|
| https://www.routledge.com/Introduction-to-Digital-Music-with...
| password4321 wrote:
| Lots of ideas two days ago:
|
| _Two years of teaching high school CS_
|
| https://news.ycombinator.com/item?id=36355172
| dybber wrote:
| 1) Make him come up with the projects to do. Use brainstorming
| techniques. Only help by guiding, not by telling him to do
| specific things
|
| 2) Build your similar own projects as well
|
| 3) Try with electronics. For that age group I have had good
| succes with MicroPython on ESP32's + various sensors/actuators.
| The first thing I do is connect an LED strip with RGB LED's and
| let them play with that.
|
| 4) Find him peers with the same interest. In that age peers are
| better partners. You can still help facilitate a bit, but the
| best would be to find a Coding club.
| lostmsu wrote:
| > Make him come up with the projects to do. Use brainstorming
| techniques. Only help by guiding, not by telling him to do
| specific things
|
| I found it difficult to do with a person who did not get how
| to use control flow and can not mentally combine multiple
| control flow constructs.
| imranq wrote:
| I had a student who was basically performing at a 6th grade math
| level despite being in 11th grade. I told that student to go
| through Khan Academy starting from Pre-K all the way to 12th
| grade and don't continue unless they achieved mastery. That
| student went from the C math student, to ultimately scoring a
| perfect score on the SAT II Math. So I highly recommend everyone
| start for the absolute basics, even if it feels like a blow to
| the ego
| cactusfrog wrote:
| The CMU database course is fire
|
| I want to make a non C++ workbook for that course to write an
| s3-based relational database (for fun), but I don't have time for
| other projects because of poor time management
| teunispeters wrote:
| As someone who could never afford to get a degree at university,
| I love this kind of stuff!
|
| I have gaps in my own knowledge, so I keep going through stuff,
| to find what I'm missing and fill it in. Eg I'm not great on O(x)
| calculations.
| tsingy wrote:
| Might interest some people looking to learn some Computer Science
| basics. It's a small aggregation of openly auditable university
| courses.
| KnobbleMcKnees wrote:
| Not sure on the prerequisites. I have absolutely no discipline
| and still managed to get my compsci degree!
| ghaff wrote:
| That probably because you were in a degree program. Discipline
| is definitely an issue if you just decide to complete a couple
| dozen courses making up a curriculum from OCW or whatever. Even
| if you take out elective stuff, especially that not connected
| to the major, you're almost certainly talking many hundreds of
| hours to plow through a college major.
| vidyesh wrote:
| I think the elective stuff might also be a reason to be able
| to successfully finish the degree. University degree for many
| comes down to studying strategically than understanding
| everything they are studying. So the elective stuff might be
| considered a break from other stuff, which means the brain
| does get time to take a break from a certain topic to retain
| that information while you study something else.
|
| Self-study is a road with very little guidance to understand
| which part is more important to study, and which just needs
| to be understood so the pressure to make sure one knows
| everything makes it difficult to progress at a consistent
| pace.
| ghaff wrote:
| >Self-study is a road with very little guidance to
| understand which part is more important to study, and which
| just needs to be understood so the pressure to make sure
| one knows everything makes it difficult to progress at a
| consistent pace.
|
| Part of it is that there's also the question of what your
| goal is.
|
| If you down an MIT CS+EE degree curriculum in OCW, you're
| actually not going to have a huge amount of programming
| except as a byproduct. If your actual objective is to learn
| front-end development, I'm guessing you won't actually have
| learned that by the time you're done. I'm guessing most
| people looking for a self-directed CS bootcamp don't
| actually want a "CS" bootcamp.
| KnobbleMcKnees wrote:
| Jokes aside, I agree. University programs do/can provide an
| almost overbearing amount of structure, and that worked well
| for me.
| hcks wrote:
| That's just the usual memes. Is this about << computer science >>
| ? Then why isn't there anything logic, algorithms, Turing
| machines, etc.. Is this << dev >>? Then what's the point of
| discrete maths?
| ke88y wrote:
| _> Is this << dev >>? Then what's the point of discrete maths?_
|
| You can probably retire on a 6% coupon if you save a lot, but
| you'll have a much more comfortable retirement if you can clip
| a 15% coupon on those same savings.
|
| Discrete Mathematics is usually some mish-mash of formal logic,
| induction, combinatorics, number theory, and baby probability.
| You can get away without knowing these things, but studying
| them doesn't take very long (14 weeks, part time?!) and pays a
| very handsome dividend. A foundation in this sort of knowledge,
| and practice operationalizing it, is often the difference
| between $60K/yr and $100K+/yr for junior developers. The size
| of the dividend payment generally increases as one's career
| progresses, assuming you stay on the IC track.
|
| Induction and formal logic are useful for reasoning about
| programs that contain loops. Often you can get away with
| intuitive understanding, and many people program for years
| before encountering problems where formal and structured
| reasoning becomes necessary (myself included!). But most well-
| paid developers will encounter a problem or two each year where
| reasoning about non-trivial loops is required and where the
| basics of induction and formal logic are tremendously helpful.
|
| Exposure to basic thinking techniques in combinatorics is
| essential for reasoning even informally about time and resource
| complexity. Writing code that relies on non-trivial time and
| resource complexity analyses is occasionally necessary in most
| well-paying developer positions.
|
| The very basics of number theory is useful for understanding,
| conceptually, how cryptography works. This isn't essential for
| most dev positions. But it is helpful knowledge.
|
| Baby probability is increasingly required knowledge for many
| dev positions, and not just because of the explosion of
| AI/ML/DS.
|
| Again, you don't need this material often. You can probably go
| an entire career avoiding the brutal pain of spending 14 weeks,
| 1-2 hours per work day, studying simple mathematics. But the
| ability to pull these skills out when they're needed is the
| difference between commodity "keep him around if we have
| billable hours" bootcamp labor and in-demand "smart and we
| really need to keep him around and eventually promote him to
| principal" labor.
| kandel wrote:
| year 1 CS in my university is
|
| :intro to CS (simple JAVA and simple coding) :linear algebra 1
| :introduction to logic (simple set theory(though the course got
| comparatively deep and proved induction as well as defined
| relations rather throughouly. most students failed.) :Digital
| systems (basic digital logic)
|
| semester 2 is: :data structures :linear algebra 2 :infitisimal
| math 1 :practical course on usages of math :combinatorics\basic
| discrete math (No generator functions or the like. Basic
| counting, basic graph theory, basic discrete probability)
|
| This is for a university that has a technical approach to CS.
| It's not considered very mathematical, so view it as a sign
| that calc1/2 and linear algebra 1/2 is needed. they are fun
| courses! Go learn the math courses with the mathematicians if
| you've felt a connection to math, there is a definite change in
| the feelings of the class. It's the "same" material but in one
| class you will think like a mathematician and in the other like
| an engineer.
| satvikpendem wrote:
| I've found Teach Yourself CS a better resource, albeit more
| advanced: https://teachyourselfcs.com
| [deleted]
| hahhahanananana wrote:
| > High School Mathematics
|
| Whenever I try to catch up with maths (in Khan Academy and
| elsewhere), I always end up in an awkward state where I keep
| recursively researching less and less advanced subjects because
| of gaps of various sizes in my fundamental knowledge. It's
| incredibly demotivating.
| vector_spaces wrote:
| I guess first consider that you might have math trauma -- read
| about it, own it (if it applies, of course), and recognize what
| it feels like when it rears its head. Lots of people -- mainly
| in the US, but it's a thing in other countries too -- were
| taught math in a pretty shitty way, often by people who don't
| want to be teaching it in the first place because they
| themselves have math trauma.
|
| Then build up fluency in the basic manipulations: do lots and
| lots and lots of exercises until those manipulations become
| second nature. You might need to start with fractions[2], and
| that's fine. One of the nice things about math at the
| elementary level is that you nearly always are guaranteed to
| get better with practice. This absolutely isn't the case for
| proof-based math, where you really need to be intentional about
| truly digesting the material and thinking careful about the
| ideas. But if you're shaky on absolute fundamentals, you can
| get incredibly far with grinding.
|
| At some point you'll need to engage with the ideas, but I think
| that's easier once you've built up some pattern recognition.
| But others will (surely) disagree
|
| [1] https://www.edweek.org/teaching-learning/opinion-how-to-
| help...
|
| [2] https://www.edweek.org/teaching-learning/fraction-phobia-
| the...
| OwlGoesHoot wrote:
| It would probably be helpful to start at a level above where
| you left off and look up specific gaps in your knowledge as you
| find them. It's always good to come to a topic with the
| understanding of every previous topic, but often those deeper
| understandings come from moving into more advanced subjects
| anyway. It might be more slow and frustrating at times, but it
| will give you a better understanding of where your specific
| gaps in knowledge actually lie and you'll be able to address
| them as you go.
| jayro wrote:
| At Math Academy, we've created a sequence of math courses
| called Mathematical Foundations I, II, & III that cover
| everything from 5th Grade Math up through Calculus I & II and
| will allow anyone to get up to speed on the skills required for
| university-level mathematics in the most efficient way
| possible. Our adaptive diagnostic exams will create a custom
| fit course no matter where you are mathematically and our
| algorithms will continually adapt to your individual strengths,
| weaknesses and learning curve.
|
| https://mathacademy.com/courses/mathematical-foundations-i
| https://mathacademy.com/courses/mathematical-foundations-ii
| https://mathacademy.com/courses/mathematical-foundations-iii
|
| In addition, we have courses on Linear Algebra and Mathematics
| for Machine Learning, with more coming soon:
|
| https://mathacademy.com/courses/linear-algebra
| https://mathacademy.com/courses/mathematics-for-machine-lear...
|
| The system is mastery based, lightly gamified, and completely
| automated. Our algorithms intelligently apply spaced-repetition
| to a hierarchical knowledge graph of over 3,000 mathematical
| concepts to make it substantially more efficient than a
| traditional course (typically on the order of 4X or more).
|
| I'm a founder and would be happy to answer any questions.
| bovem wrote:
| It might not be the same for you. But this is what I enjoy when
| I study anything. Filling up the gaps in my knowledge and
| learning about new ways to think or understand about a concept.
| Maybe you shouldn't dive so deep into the concepts. Just write
| all the topics/concepts you didn't understand while learning
| something and watch one video about each of them.
| danielvaughn wrote:
| Weirdly enough, mathematics is a very emotional subject for me.
| I never understood how it was taught in school, and had serious
| difficulty understanding it. As a result I just ignored it,
| believing that I didn't have the right brain for it.
|
| Even though I taught myself how to code, I never went back and
| learned math, so my level of knowledge is at a basic high
| school level. It can be embarrassing at times, and every now
| and then I think about trying to learn it.
| wonderingwhale wrote:
| I honestly think this is one of the bigger problems with
| people who "can't do math", probably most people can learn
| quite a bit of (at least basic) mathematics. But oftentimes
| when you did not understand the subject well previously, like
| in high school because of different interests at the time or
| a bad teacher or something. And then because of this whenever
| you see an equation or hear the word 'mathematics' you just
| shut off your brain. I know some people who can understand me
| when I explain some physics or mathematics concept without
| explicit mathematics, but they would be scared off at the
| first equation.
| vidyesh wrote:
| Too many false starts too lead to doing the same fundamentals
| all over again, making one feels like they are not progressing
| at all.
|
| I remember reading somewhere, do the implementation of it along
| side fundamentals. The reason you are studying fundamentals to
| progress ahead, do that course along side too. This helps one
| grasp the fundamentals quickly and more importantly to know
| which fundamentals you really need than to try to do everything
| and forget aspects of it later.
|
| That being said, I am yet to implement that concept and get
| over false starts
| ke88y wrote:
| Paradoxically, self-teaching is most difficult at the "101" and
| "pre-101" level. Once you have the basics, self-teaching
| becomes much easier.
|
| Teaching yourself Calculus I and Calculus II after obtaining
| High School mathematical literacy is not too bad. Teaching
| yourself Differential Equations or even Functional Analysis
| after obtaining the pre-reqs is actually quite easy. But
| teaching yourself high school or especially middle school
| mathematics requires a TON of dedication.
|
| It's not impossible, of course, but "The Basics" are where you
| _really_ benefit from the help of a professional educator.
|
| For this reason, I recommend eschewing self-directed resources
| and enrolling in an "Applied Math" or "College Algebra" course
| at your local community college. These courses are basically
| "high school mathematics for people who never learned or forgot
| high school mathematics". Depending on where you live, the
| "College Algebra" course at your local Community College is
| probably very cheap or free and available as an evening and/or
| online course. You usually do not need to enroll in a degree
| program to take the course.
|
| Once you make it through "College Algebra" you can return to
| self-directed learning.
|
| Community Colleges are a vastly under-utilized resource,
| particularly for these "very fundamental knowledge gaps" where
| self-directed learning is much more difficult.
| yt-sdb wrote:
| Maybe 5 years ago, I was in a similar place. I had a
| particularly embarrassing moment at work when it clicked that I
| just... didn't know the basics. I was, to use an overused term,
| "mathematically immature".
|
| So I made a commitment: I decided I would work through Khan
| Academy math for 1-hour a day for 1 year. I started with pre-K
| [1] (specifically counting) and watched every video and did
| every single exercise in order. I focused on mastery. I didn't
| rush myself, and I did not continue until I felt completely
| confident in the material. I just did this for a year. I think
| I go through roughly algebra 2. In my mind, it is critical to
| combine explicit knowledge (watch videos) with tactic knowledge
| [2] (do exercises). For example, you need to understand what a
| logarithm is conceptually but you also just need to do problems
| to get a feel for it. So this is fundamentally different than
| learning-by-grazing or just reading a book.
|
| I could go on and on, but let me just say that it changed my
| relationship to math in a deep way.
|
| [1] https://www.khanacademy.org/math/k-8-grades [2]
| https://commoncog.com/tacit-knowledge-is-a-real-thing/
| xwowsersx wrote:
| What did you do after you completed the K-8?
| yt-sdb wrote:
| I worked from the top of this page [1] downwards and ended
| after algebra 2.
|
| [1] https://www.khanacademy.org/math
| noSyncCloud wrote:
| This is really inspiring, thanks for sharing. I should do
| likewise. I wound up dropping out of school (had kids too
| early, don't ask), which was... not a good decision. I do
| work as a developer but I need more domain knowledge in
| mathematics. Never too late to start, I guess.
| gareve wrote:
| if you would have to do it again, would you change something
| on your methodology? I assume there were some unnecessary
| time sinks here & there
| gpt5 wrote:
| If you, or someone else is seriously considering learning
| math from the basic at a high level, I'd recommend picking
| up "art of problem solving, pre-algebra" book, and walking
| up from there.
|
| These sets of books are universally considered to be among
| the best math education resources by mathematicians and
| others, and they start from the very basic (such as the
| number line and basic operations), but without the need of
| practicing elementary school material like counting.
| jacksnipe wrote:
| I think the TAOPS curriculum would be incredibly
| challenging for somebody who has actively incorrect
| intuitions about math.
| yt-sdb wrote:
| I don't think so. My problem was that I had a weak grasp of
| many basics concepts, and more critically I did not know in
| which areas I was weak. So while it's easy ex post to say
| "I could skip such and such section", it would have been
| impossible to make this judgment ex ante.
|
| And in fact, I think a failure mode many people make is
| trying to predict which things they already know and then
| skipping those. This allows for blind spots to persist.
|
| I suppose the one way to skip things correctly would be to
| have a coach. But that comes at a new cost ($), but maybe
| that works for some people.
| hawk_ wrote:
| I have been seeing more and more usage of 'ex post' and
| 'ex ante' lately. What do they convey that isn't conveyed
| by 'after' and 'before'?
| yt-sdb wrote:
| "Before" and "after" are generic terms. A car might stop
| before the crosswalk (space). You might eat dinner after
| work (time). But "ex ante" and "ex post" specify a
| relationship to an (random) event or to specific
| information. For example, a data scientist might compute
| a quantity "ex ante". This means that the quantity was
| estimated using only forecast data. No historical data
| was used. It would not make sense, however, to say that a
| car stops ex ante the crosswalk.
|
| I could have easily said "afterwards" and "beforehand",
| but I like "ex post" and "ex ante" when referring to
| before/after having access to specific information.
| hawk_ wrote:
| Got it. I will try to leverage the synergies between
| Latin and English ex post.
| timidiceball wrote:
| it conveys that you know what ex post and ex ante mean
| jhardy54 wrote:
| Or, quite often, conveys that you don't know what they
| mean.
| status200 wrote:
| This is inline with a Zen practice called "beginner's mind",
| and is so useful in many areas, thank you for this
| inspiration.
| randmeerkat wrote:
| > Whenever I try to catch up with maths (in Khan Academy and
| elsewhere), I always end up in an awkward state where I keep
| recursively researching less and less advanced subjects because
| of gaps of various sizes in my fundamental knowledge. It's
| incredibly demotivating.
|
| Try this course: https://www.edx.org/course/college-algebra-
| and-problem-solvi...
|
| It uses the ALEKS system which identifies your weak points and
| brings you up to speed. Take notes during the process so you
| have something to reference in the future and won't forget what
| you learned.
|
| After you knock out the algebra course you'll be ready for the
| precalculus course: https://www.edx.org/course/precalculus
|
| The ALEKS system in the Precalculus course will also remediate
| anything you forgot from the Algebra course.
|
| Hopefully this will help give you the confidence to go after
| more advanced maths once you finish both courses. Be kind to
| yourself, math, like anything, is a skill, it takes time and
| practice.
| satvikpendem wrote:
| Why not start from the beginning, ie pre-K on up, as the other
| commenter mentioned? I've done something similar for teaching
| myself web development (since it's not taught often in CS
| degree programs), starting from bare HTML, adding CSS, adding
| Javascript, adding TypeScript, adding React, and so on. Now I
| have a good foundation from which to build anything I want. So
| too with mathematics or really any subject.
| glass-z13 wrote:
| Same for me, let me know if you find the solution! I think it's
| extremely hard to get into this kind of stuff when you
| basically have to start from 0 meanwhile everyone else has a
| better foundation than you
| Cerium wrote:
| Have you seen "An Infinitely Large Napkin"? I saw it posted
| here a couple years ago. It is Evan Chen's project "aimed at
| making higher math accessible to high school students."
|
| https://web.evanchen.cc/napkin.html
| tsingy wrote:
| The book that made things click for me was Maths: A Student's
| Survival Guide by Jenny Olive. Give it a shot, use a calculator
| for everything. IMO in the age of computers let computers do
| the calculations and just learn to have intuitions.
| ghaff wrote:
| I'd have to be convinced that you can develop those
| intuitions without basic arithmetic. Mind you, I'm not saying
| spend a lot of time mastering long division or whatever. (I'd
| probably have to look up the technique myself.) But I think
| some level of numeric fluency is probably necessary.
| 2devnull wrote:
| "I'd probably have to look up the technique myself."
|
| No offense but I am pretty sure that was the point. If it's
| math you forget, it's not math worth learning. Learn what
| you want or need to know. The rest is dross.
| poulsbohemian wrote:
| My 13 year old is a very good student, currently taking high
| school math classes while in middle school... one of the things
| that the public school system hasn't figured out is how to make
| any of it relevant. So sure, she's brilliant and flies through
| the material, but she'd be the first to tell you it's just
| puzzles, it has no actual meaning to her. I was the opposite -
| because it had no meaning to me, I couldn't understand it and
| was a terrible math student. But, once I could view it through
| the lens of computer science, suddenly it had meaning and I did
| fine.
|
| My oldest daughter was a terrible student. But she would say to
| me "If they taught history class the way you explain historical
| events around the dinner table, I would have been a lot more
| interested in studying."
|
| So point being - it's probably not you, a lot of it really is
| the way we approach k-12 education. In hindsight, I'm not sure
| college is any better and may be worse what with the approach
| of hazing and weeding out.
| gnicholas wrote:
| The Khanmigo chatbot that KA is rolling out supposedly helps
| with this problem of relevance.
| ranieuwe wrote:
| I have the same problem and have still not found a workable
| solution.
|
| Only one there seems to be is to basically rerun 12 years of
| math, which is really unpleasant because I know 80% of the work
| making it unrewarding and slow. I don't know what I don't know
| that is super demotivating, indeed.
| xwowsersx wrote:
| Another resource I wanted to mention here is OpenStax.
| Specifically, their Prealgebra book:
| https://openstax.org/details/books/prealgebra-2e it's a fully
| online-native book format with exercises, etc.
| EGreg wrote:
| For what it's worth, if you want to go bottom-up and give
| yourself a super-solid foundation, go through the videos I
| recorded several years ago specifically for this purpose. They
| are for children as well as adults:
| https://www.youtube.com/@thinkingmathematically
|
| Please let me know if they were helpful!
| EGreg wrote:
| Is this like Poor Richard's Almanac?
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